Optical material, optical element, and method for manufacturing same

ABSTRACT

An optical material which has a relative permeability different from 1 to light having a wavelength in, for example, the infrared region or shorter than the infrared region and which is stable in structure, and a liquid and a solid (optical element) using the optical material. The optical material is a powder used as a component of a liquid or solid to which an illuminating light is irradiated, and includes a large number of resonating elements which constitute the powder and each of which is formed of a conductor having a width approximately same as or smaller than a wavelength of the illumination light, and a protective film which is formed of a disc-shaped insulator, wherein an entire surface of each of the split-rind resonators is covered by the protective film.

This application is a Divisional application of U.S. application Ser.No. 13/248,331 filed on Sep. 29, 2011, which is a Continuationapplication of International Application No. PCT/JP2010/056403 which wasfiled on Apr. 8, 2010 claiming the conventional priority of U.S.Provisional Application Ser. No. 61/202,845 filed on Apr. 10, 2009,Japanese Patent Application Nos. 2009-243438 filed on Oct. 22, 2009 and2009-243439 filed on Oct. 22, 2009, all of the disclosures of which areincorporated herein by reference in their entirety.

TECHNICAL FIELD

The present teaching relates to an optical material which is used as acomponent (a part or a portion) of a liquid or solid to which anillumination light (illumination light beam) is irradiated, an opticalliquid and an optical element which include the optical material, amethod for producing the optical material and a method for producing theoptical liquid and the optical element. More specifically, the presentteaching relates to, for example, an optical material having relativepermeability which is different from 1 (one).

BACKGROUND ART

Optical materials such as conventional optical glass all have a relativepermeability that is approximately 1 and have a relative permittivitythat is greater than 1, and thus have refractive index with a positivevalue greater than 1. In view of this situation, researches are madewith respect to so-called meta-materials that are substances providedwith a structure smaller than the wavelength of a light as an objectiveto which the meta-materials are to be applied and greater than an atomor molecule and exhibiting a relative permeability value and/or relativepermittivity value which are/is unobtainable with a substance in thenatural world. Further, with respect for example to a microwave having awavelength of 6 cm (frequency: 5 GHz), a large number of smallsplit-ring resonators having a negative relative permeability and alarge number of thin metallic lines having a negative relativepermittivity and arranged in parallel are combined and thus a substance(structure) having a negative refractive index is realized (see, forexample, Non-patent Literature 1).

In the recent years, in order to realize a substance having a negativerefractive index to lights in the infrared to visible regions, forexample, such a substance is theoretically proposed having a pluralityof minute split-ring resonators and a relative permeability that isgreatly different from 1 (including a negative value) with respect to alight of which wavelength is about 1,000 nm to about 400 nm (see, forexample, Non-patent Literature 2). By combining the minute split-ringresonators (having the relative permeability in a negative range) andanother substance having a negative relative permittivity, it ispossible to realize the substance having the negative refractive indexto the lights in the infrared to visible regions.

CITATION LIST Non-Patent Literature [Non-Patent Literature 1]

-   D. R. Smith et al.: “Composite medium with simultaneously negative    permeability and permittivity”, Phys. Rev. Lett. (the United    States), 84, pp. 4184-4187 (2000).

[Non-Patent Literature 2]

-   A. Ishikawa, T. Tanaka and S. Kawata: “Frequency dependence of the    magnetic response of split-ring resonators”, J. Opt. Soc. Am. B (the    United States), Vol. 24, No. 3, pp. 510-515 (2007).

SUMMARY

According to a first aspect of the present teaching, there is providedan optical material which is used as a component of a liquid or solid towhich an illumination light is irradiated, the optical materialcomprising:

a plurality of minute resonators each of which is formed of a conductorhaving a width approximately same as or smaller than a wavelength of theillumination light; and

a protective film which is formed of an insulator or a semi-conductor,wherein each of the minute resonators is covered by the protective film.

According to a second aspect of the present teaching, there is providedan optical material which is used as a component of a liquid or solid towhich an illumination light is irradiated, the optical materialcomprising a plurality of resonating elements each of which includes:

a plurality of minute resonators each of which is formed of a conductorhaving a width approximately same as or smaller than a wavelength of theillumination light and which are arranged apart from each other; and

a protective film which is formed of an insulator or a semi-conductorand which covers the minute resonators.

According to a third aspect of the present teaching, there is providedan optical liquid comprising a liquid; and the optical material of thefirst or second aspect of the present teaching which is mixed in theliquid.

Further, according to a fourth aspect of the present teaching, there isprovided an optical element comprising the optical material of the firstor second aspect of the present teaching which is solidified.

Furthermore, according to a fifth aspect of the present teaching, thereis provided a method for producing an optical material composed of aplurality of minute resonators each of which is formed of a conductor,and is covered by a protective film formed of an insulator or asemi-conductor, the method comprising the steps of:

forming a sacrifice layer on a substrate;

forming a first protective layer formed of the insulator or thesemi-conductor on the sacrifice layer;

forming a conductive layer formed of the conductor on the firstprotective layer;

patterning the minute resonators in the conductive layer;

forming a second protective layer formed of the insulator or thesemi-conductor so as to cover the patterned minute resonators; and

removing the sacrifice layer.

According to a sixth aspect of the present teaching, there is provided amethod for producing an optical material having a plurality of opticalelements each of which is composed of a plurality of minute resonatorsformed of a conductor and is arranged apart from each other, and whichare covered by a protective film formed of an insulator or asemi-conductor, the method comprising the steps of:

forming a sacrifice layer on a substrate;

forming a first protective layer formed of the insulator or thesemi-conductor on the sacrifice layer;

forming a first conductive layer formed of the conductor on the firstprotective layer;

patterning the minute resonators in the first conductive layer;

forming a second protective layer formed of the insulator or thesemi-conductor so as to cover the patterned minute resonators;

removing a part of the first protective layer and a part of the secondprotective layer based on an arrangement of the minute resonators ineach of the optical elements; and

removing the sacrifice layer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(A) is a perspective view of powder of an optical material of afirst embodiment, FIG. 1(B) is an enlarged perspective view of aplurality of resonating elements 14 (each of which is a split-ringresonator (SRR) covered by a protective layer) constructing the powder,and FIG. 1(C) is an enlarged perspective view showing one SRR.

FIG. 2 is a diagram showing an example of relative permeability of theSRR.

FIG. 3 is a flowchart showing an example of a method for producing alarge number of the resonating elements 14.

FIG. 4(A) is a diagram showing an exposure apparatus which is used in anexposure step, FIG. 4(B) is an enlarged plan view of a part of a patternof a first reticle, and

FIG. 4(C) is an enlarged plan view of a part of a pattern of a secondreticle.

FIG. 5 (FIGS. 5(A) to 5(G)) is an enlarged cross-sectional view showinga construction of a part of a wafer in a plurality of steps duringproduction process until a large number of the resonating elements 14are produced.

FIG. 6(A) is a diagram showing a liquid in which a large number of theresonating elements 14 are mixed, FIG. 6(B) is an enlarged view of a Bportion shown in FIG. 6(A), FIG. 6(C) is a diagram showing an opticallens including a large number of the resonating elements 14, and FIG.6(D) is an enlarged view of a D portion shown in FIG. 6(C).

FIG. 7(A) is an enlarged perspective view of a resonating element 14 ofa first modification, and FIG. 7(B) is an enlarged perspective view of asplit-ring resonator 17 shown in FIG. 7(A).

FIG. 8(A) is an enlarged plan view of a part of a pattern of a reticleR1A which is used in a second modification, FIG. 8(B) is an enlargedplan view of a part of a pattern of a reticle R1B.

FIG. 9(A) is an enlarged perspective view of a resonating element 14B ofa third modification, and FIG. 9(B) is an enlarged plan view of a partof a pattern of a reticle which is used for producing the resonatingelement 14B.

FIG. 10(A) is an enlarged perspective view of a resonating element 14Cof a second embodiment, FIG. 10(B) is a side view of the resonatingelement 14C shown in FIG. 10(A), and FIG. 10(C) is a perspective view ofpowder of an optical material of the second embodiment.

FIG. 11(A) is an enlarged perspective view of another resonating element14D of the second embodiment, FIG. 11(B) is a side view of theresonating element 14D shown in FIG. 11(A).

FIG. 12(A) is an enlarged perspective view of a plurality of split-ringresonators (SRRs) in the resonating element 14D, and FIG. 12(B) is anenlarged perspective view of one SRR.

FIG. 13 (13A, 13B) is a flowchart showing an example of a method forproducing the resonating elements 14C, 14D.

FIG. 14(A) is an enlarged view of a pattern for SRR, FIG. 14(B) is anenlarged plan view of a part of a pattern of a first reticle, and FIG.14(C) is an enlarged plan view of a part of a pattern of a secondreticle.

FIG. 15 (FIGS. 15(A) to 15(G)) is an enlarged cross-sectional viewshowing a construction of a part of the upper surface of a wafer in aplurality of first half steps during a process for producing theresonating element 14D.

FIG. 16 (FIGS. 16(A) to 16(G)) is an enlarged cross-sectional viewshowing the construction of the part of the upper surface of the waferin a plurality of latter half steps during the process for producing theresonating element 14D.

FIG. 17(A) is an enlarged perspective view of a resonating element 14Eof a modification, and FIG. 17(B) is an enlarged plan view of a part ofa pattern of a reticle for producing the resonating element 14E.

DESCRIPTION OF THE EMBODIMENTS First Embodiment

A preferred first embodiment of the present teaching will be explainedwith reference to FIGS. 1 to 6.

FIG. 1(A) shows powder 12 of an optical material of the embodiment, FIG.1(B) is an enlarged perspective view of a plurality of resonatingelements 14 which are a part or portion composing the powder 12 and eachof which is a split-ring resonator covered by a protective layer. In thefollowing description, the split-ring resonator is also referred to as“SRR”. In FIG. 1(B), each of the plurality of resonating elements 14 isformed or constructed, for example, by covering entire faces of a splitring-shaped SRR (split-ring resonator) 16, which is made of a metal suchas silver (Ag), gold (Au), copper (Cu), aluminum (Al) or the like, witha protective layer 18 having a disc-shape and formed of an insulator(insulating material) such as silicon dioxide (SiO₂), aluminum oxide(Al₂O₃), or the like. Note that the protective layer 18 may have, forexample, a square plate-shape.

In FIG. 1(B), two resonating elements 14 adjacent in the x-direction andthe y-direction are periodically arranged with a period of “a” and tworesonating elements 14 adjacent in the z direction are periodicallyarranged with a period of “b” in the rectangular coordinate system (x,y, z). Note that the arrangement state of the plurality of resonatingelements 14 in FIG. 1(B) is a virtual arrangement for calculating therelative permeability (to be discussed later), and a large number of theresonating elements 14 in the powder 12 shown in FIG. 1(A) are randomlyarranged. In this embodiment, since each of the SRRs 16 is covered bythe protective layer 18, average spacing distances or gaps (arrangementperiods) of the plurality of SRRs 16 in the lateral and thicknessdirections thereof respectively are substantially defined by an outershape of the protective layer 18.

FIG. 1(C) shows one of the SRRs (split-ring resonators) 16 in oneresonating element 14 as shown in FIG. 1(B). In FIG. 1(C), the SRR 16 isconstructed of four fan-shaped members 16A, 16B, 16C and 16D obtained bysplitting or dividing a ring, of which center is an axis parallel to thez axis, in the circumference direction of the circle with a spacingdistance g. Note that a split number N (N=2, 3, 4, 5, . . . ) by whichthe SRR is split is arbitrary, and the SRR 16 may be constructed of aplurality of arbitrary number of fan-shaped members.

The inner diameter of the SRR 16 is r (diameter is 2r), the width in theradial direction of the SRR 16 is w, the thickness of the SRR 16 is T.In this case, according to the document by A. Ishikawa, T. Tanaka and S.Kawata and entitled “Frequency dependence of the magnetic response ofsplit-ring resonators”, J. Opt. Soc. Am. B (the United States), Vol. 24,No. 3, pp. 510-515 (2007) (hereinafter referred to as “ReferenceLiterature A”), an effective relative permeability μeff of the pluralityof SRRs 16 arranged as shown in FIG. 1(B) with respect to anillumination light having a predetermined wavelength λ (angularfrequency is ω) is as follows. The real part of the relativepermeability is μRe, the imaginary part of the relative permeability isμIm, and i is the imaginary unit.

$\begin{matrix}{{\mu_{eff} = {{\mu_{Re} + {\mu}_{Im}} = {1 - \frac{F\; \omega^{2}}{\omega^{2} - \frac{1}{CL} + {\frac{{Z(\omega)}\omega}{L}}}}}},} & (1)\end{matrix}$

Further, provided that the space permeability (vacuum permeability) isμ₀, the permittivity is ∈₀, and the relative permittivity of the SRR 16is ∈r, then the parameters F, C, L and the impedance Z (ω) in theformula (1) are represented as follows:

$\begin{matrix}{{F = \frac{\pi \; r^{2}}{a^{2}}},} & (2) \\{{C = {\frac{1}{N}\varepsilon_{0}\varepsilon_{r}\frac{wT}{g}}},} & (3) \\{{t = \frac{g}{{2\; w} + g}},} & (4) \\{{L = \frac{\mu_{0}\pi \; r^{2}}{b}},} & (5) \\{{{Z(\omega)} = \frac{2\pi \; {{rZ}_{s}(\omega)}}{w}},} & (6) \\{{Z_{s}(\omega)} = {{R_{s}(\omega)} + {\; {X_{s}(\omega)}}}} & (7)\end{matrix}$

Note that in this embodiment, the parameter t in the formula (4) is notused. Further, the split number N in the formula (3) is 4 regarding theSRR 16; Rs(ω) in the formula (7) is the surface resistance of the SRR 16and Xs(ω) in the formula (7) is the inner reactance of the SRR 16; andas disclosed in Reference Literature A, in a case that, for example, thewavelength λ is in the visible region, the Rs(ω) takes a value in arange from about 0.2 to about 1.7 depending on the material of the SRR16, and the Xs(ω) takes a large negative value regardless of thematerial.

Further, according to the formula (1), the real part μRe of theeffective relative permeability μeff becomes considerably greater than 1in predetermined ranges in each of which a frequency f [THz] of theillumination light is smaller than a predetermined resonance frequency(f1, f2, f3, etc.) and takes a negative value in predetermined ranges ineach of which the frequency f is greater than the predeterminedresonance frequency, as shown in FIG. 2, depending on the shape andarrangement of the SRRs 16. Furthermore, as the resonance frequency fbecomes higher from f1 to f3, the absolute value of the real part μRebecomes smaller. Note that the resonance frequency is substantiallydefined by the parameters of the shape of SRR 16 (r, w, T, etc.), andthe contribution by the arrangement periods a, b of the SRRs 16 areconsidered as relatively small.

According to Reference Literature A, in a case that the radius r of theSRR 16 is same as the width w of the SRR 16, that the period b is 350nm, the spacing distance g is 33 nm, the thickness T is 2.5 times thepenetration depth, and the relative permittivity ∈r is 2.25, theresonance frequency f1 is 300 THz (the wavelength λ1 correspondingthereto is 1000 nm (1 μm)), the resonance frequency f2 is 500 THz (thewavelength λ2 corresponding thereto is 600 nm), and the resonancefrequency f3 is 700 THz (the wavelength λ3 corresponding thereto is 420nm). Namely, the wavelength λ1 corresponding to the resonance frequencyf1 is in the infrared region, the wavelengths λ2, λ3 corresponding tothe resonance frequencies f1, f2, respectively are in the visibleregion.

Further, in the formulae (1) to (5), when the resonance frequency f1(wavelength λ1: 1000 nm) can be obtained, the period a, the radius r andouter diameter 4r (which is the width of the outer diameter) of the SRR16 (=2(r+w)), are 875 nm, 125 nm and 600 nm, respectively. Furthermore,when the resonance frequency f2 (wavelength λ2: 600 nm) can be obtained,the period a, the radius r and the outer diameter 4r are 525 nm, 75 nmand 300 nm, respectively; and when the resonance frequency f3(wavelength λ3: 420 nm) can be obtained, the period a, the radius r andthe outer diameter 4r are 350 nm, 50 nm and 200 nm, respectively. Inthis case, since the thickness T of the SRR 16 is about the radius r orthinner than the radius r, the maximum width of the outer shape of theSRR 16 is 4r and the size of the outer shape of the SRR 16 (maximumwidth (4r)) is approximately ½ of the wavelength λ1 to λ3 correspondingthereto.

Moreover, in the embodiment, in a case that the relative permeability ofthe protective layer 18 is approximately 1 and the resonating element 14is used as a substance having the real part μRe of the relativepermeability that is considerably greater than 1 (for example, greaterthan 2), the wavelength of the illumination light may be set to λ1 b, λ2b (frequencies f1 b, f2 b corresponding thereto are lower than theresonance frequencies f1, f2), etc. in a range slightly longer than λ1,λ2 (similarly regarding λ3 as well). On the other hand, in a case thatthe resonating element 14 is used as a substance having the real partμRe of the relative permeability that is negative, the wavelength of theillumination light may be set to λ1 a, λ2 a (frequencies f1 a, f2 acorresponding thereto are higher than the resonance frequencies f1, f2),etc. in a range slightly shorter than λ1, λ2. By doing so, theresonating element 14 can be used as a substance (meta-material) inwhich the real part μRe of the relative permeability is considerablydifferent from 1.

As an example shown in FIG. 6(A), a large number of the resonatingelements 14 may be mixed (or dissolved) in a predetermined solvent tothereby produce an optical liquid 30. As shown in FIG. 6(B) which is anenlarged view, the liquid 30 is obtained, for example, by mixing(dissolving) a large number of the resonating elements 14 in a solvent30 a such as a pure water (purified water). Further, in a case that thesolvent 30 a is water (relative permittivity is positive), theresonating elements 14 are used, for example, under a condition that thewavelength is set to be λ1 b or λ2 b, etc. with which the real part μReof the relative permeability is considerably greater than 1 as shown inFIG. 2. Under this condition, since the refractive index of the water 30takes a value that is greater than, for example, 2, the liquid 30 can beused as a liquid having a high refractive index. Such a liquid havingthe high refractive index is usable, for example, as an immersion liquidfor a liquid immersion type microscope, an immersion liquid for a liquidimmersion type exposure apparatus (to be described later on), etc. Theorientations (directions) of the respective resonators mixed in theliquid are random, and thus the liquid can have an isotropic opticalcharacteristic.

Further, in a case that the solvent 30 a is, for example, a liquidhaving a negative relative permittivity, the resonating elements 14 areused under a condition, for example, that the wavelength is set to be λ1a or λ2 a, etc. with which the real part μRe of the relativepermeability is negative as shown in FIG. 2. Under this condition, therefractive index of the liquid 30 takes a negative value. Such a liquidhaving the negative refractive index is, for example, filled in a celland thus becomes usable as a super lens such as an optical elementhaving a negative refractive index, as will be described later on.

Furthermore, as shown in FIG. 6(C) as another example, a plate-shapedoptical element 32 can be produced by solidifying the large number ofresonating elements 14. As shown in FIG. 6(D) that is an enlarged view,the optical element 32 is obtained, for example, by mixing a medium 32 ain a powdery form (filling agent) and the powder of the resonatingelements 14 uniformly and then by solidifying the mixture by means ofsintering, etc. Further, in a case that the protective layer 18 of eachof the resonating elements 14 is formed of silicon dioxide (havingpositive relative permittivity) in a state that the medium 32 a isabsent, then the resonating elements 14 are used under a condition thatthe wavelength is set to be λ1 b or λ2 b, etc. with which the real partμRe of the relative permeability is considerably greater than 1 as shownin FIG. 2. Under this condition, since the refractive index of theoptical element 32 takes, for example, a value greater than 2, it ispossible to produce an optical lens having, for example, a refractiveindex greater than 2 by processing the optical element 32 into aspherical or aspherical lens.

On the other hand, in a case that the medium 32 a is, for example, asubstance having a negative relative permittivity (for example, a largenumber of minute thin metallic lines, or a dielectric having a smallbandgap), the resonating elements 14 are used under a condition, forexample, that the wavelength is set to be λ1 a or λ2 a, etc. with whichthe real part μRe of the relative permeability is negative as shown inFIG. 2. Under this condition, the refractive index of the opticalelement 32 takes a negative value. When an illumination light IL comesinto such an optical element 32 having the negative refractive indexfrom an external object point 34 as shown in FIG. 6(C), then theillumination light IL is imaged precisely to an external image point 36.Accordingly, the optical element 32 can be used as a so-called superlens.

Next, an example of a method for producing the powder 12 composed of thelarge number of resonating elements 14 as shown in FIG. 1(A) will beexplained with reference to a flow chart shown in FIG. 3. This producingmethod uses a photolithography step, and an exposure apparatus 50 shownin FIG. 4(A) is used in the photolithography step.

In FIG. 4(A), the exposure apparatus 50 which is a scanning-exposure andliquid immersion type and is constructed of a scanning stepper includes,for example, an exposure light source (not shown) which generates anillumination light or illumination light beam (exposure light orexposure light beam) IL such as, for example, an ArF excimer laser(wavelength: 193 nm) or a KrF excimer laser (wavelength: 248 nm), etc.;an illumination optical system ILS which illuminates a reticle R1 (or areticle R2, etc.) with the illumination light IL; a reticle stage RSTwhich moves (scans) the reticle R1, etc.; a projection optical system PLwhich projects a pattern of the reticle R1, etc., onto a wafer P at apredetermined projection magnification β (for example, a reductionmagnification of ¼, etc.); and a wafer stage WST which moves (scans andstep-moves) the wafer P in a plane perpendicular to an optical axis AXof the projection optical system PL. The wafer P is, for example, adisc-shaped substrate (base member) having a diameter of 200 mm, 300 mmor 450 mm, etc., and formed of silicon, etc., and a predeterminedplurality of numbers of layers of thin films and a photoresist(photosensitive material) are formed on the wafer P.

The exposure apparatus 50 is further provided with a local immersionmechanism including a nozzle head 51 which is arranged to surround a tip(end) portion of an optical member located at the lower end of theprojection optical system PL; a liquid supply device 52 which supplies aliquid Lq such as a pure water (purified water) allowing theillumination light IL to transmit therethrough to a local space betweenthe wafer P and the optical member arranged inside the nozzle head 51;and a liquid recovery device 53 which recovers the liquid Lq in thelocal space. Note that as the local liquid immersion mechanism, it isallowable to use, for example, the mechanism as disclosed in UnitedStates Patent Application Publication No. 2007/242247 or European PatentApplication Publication No. 1420298, etc. Further, as the liquid Lq, itis also allowable to use the liquid 30 shown in FIG. 6(A) (in a casethat the liquid is used in the wavelength region at which the liquid 30exhibits a high refractive index).

As described above, the exposure apparatus 50 is a liquid immersion-typeexposure apparatus. Therefore, it is possible to produce the SRR(split-ring resonator) 16 in FIG. 1(C) having the radius r of about 50nm easily and highly precisely.

Further, FIG. 4(B) is an enlarged plane view showing a part or portionof a pattern formed in a pattern area in the reticle R1 shown in FIG.4(A). In FIG. 4(B), a first pattern 55, which is formed of alight-shielding film and which is magnification of the SRR 16 shown inFIG. 1(C) by the reciprocal ratio of the projection magnification β, isformed in the pattern area in the reticle R1 in mutually orthogonal twodirections at a predetermined period.

FIG. 4(C) is an enlarged plan view showing a part or portion of apattern formed in the reticle R2 shown in FIG. 4(A). In FIG. 4(C), asecond pattern 57, which is formed of a light-shielding film and whichis magnification of the outer shape of the protective layer 18 of theresonating element 14 shown in FIG. 1(B) by the recipriocal ratio of theprojection magnification β, is formed in the pattern area of the reticleR2 in mutually orthogonal two directions at a predetermined period whichis same as the arrangement period for the first pattern 55. During theexposure, the second pattern 57 on the reticle R2 is positioned at alocation same as a location 55A at which the first pattern 55 on thereticle R1 is arranged. Further, an area 58 between the second patterns57 on the reticle R2 corresponds to a separation band for separating theplurality of resonating elements 14 away from one another.

Further, in Step 101 of FIG. 3, one lot of wafers each of which is, forexample, a silicon wafer having a disc-shape and diameter of 300 mm isprepared. Although the following processes or steps are sequentiallyexecuted for processing the one lot of wafers, the processes will beexplained as follows regarding one piece of the wafers P. FIGS. 5(A) to5(G) are each an enlarged cross-sectional view showing a part of theconstruction of a multi-layered thin film (plurality of layered thinfilms) formed on the wafer P. At first, in a thin-film forming apparatus(not shown), a first photoresist layer 22A is formed on an entiresurface of the wafer P as shown in FIG. 5(A). The first photoresistlayer 22A is used not as a photosensitive layer for forming a resistpattern, but is used as a sacrifice layer for separating the largenumber of resonating elements 14 away from the wafer P at the end of theprocesses.

Next, in Step 102, a first silicon dioxide (SiO₂) layer 24A is formed onthe first photoresist layer 22A on the wafer P. Then, in Step 103, ametallic thin film 26 made of a metal (in this case, for example, silveror aluminum, etc.) is formed on the first silicon dioxide layer 24A.Next, in Step 104, a second, positive-type photoresist layer 22B isformed on the metallic thin film 26. The second photoresist layer 22Band the first photoresist layer 22A are different types from each other,and the first photoresist layer 22A is not dissolved by a developingliquid and a dissolving liquid for the second photoresist layer 22B (anda photoresist layer 22C which will be described later on). Next, in Step105, the wafer P is loaded on the exposure apparatus 50 shown in FIG.4(A), and the second photoresist layer 22B in each of all the shot areason the wafer P is exposed with a pattern of the minute SRR (split-ringresonator) composed of a large number of images 55P of the firstpatterns 55 of the reticle R1, by the exposure apparatus 50. Note thatin this example, in FIG. 5(A), areas between the large number of images55P are exposed by the illumination light.

Next, in Step 106, the wafer P is transported to a coater/developer (notshown), and the second photoresist layer 22B on the wafer P isdeveloped. By doing so, a resist pattern 22BP corresponding to thepattern of the SRR is formed, as shown in FIG. 5(B). Next, in Step 107,the wafer P is transported to an etching device (not shown) and themetallic thin film 26 on the wafer P is etched with the resist pattern22BP serving as a mask, thereby forming a large number of minute SRRs 16as shown in FIG. 5(C). Then, the resist pattern 22BP is removed.

Next, in Step 108, the thin-film forming apparatus (not shown), a secondsilicon dioxide layer 24B is formed so as to cover the large number ofminute SRRs 16 on the wafer P, as shown in FIG. 5(D). Then, in Step 109,a third, positive-type photoresist layer 22C is formed on the secondsilicon dioxide layer 24B of the wafer P at the coater/developer (notshown). Next, in Step 110, the wafer P is loaded on the exposureapparatus 50 shown in FIG. 4(A), and the third photoresist layer 22C onthe wafer P is exposed with images 57P of the second patterns 57 of thereticle R2, by the exposure apparatus 50. By doing so, the area(separation band) between the large number of SRRs 16 on the wafer P isexposed. After that, the third photoresist layer 22C on the wafer P isdeveloped in the coater/developer (not shown). With this, as shown inFIG. 5(E), a resist pattern 22CP is formed at an area at which theprotective layer 18 as shown in FIG. 1(B) is to be formed, so as tocover the large number of the SRRs 16 on the wafer P.

Next, in Step 111, the first and second silicon dioxide layers 24A, 24Bare etched at the etching device (not shown) with the resist pattern22CP on the wafer P serving as a mask, as shown in FIG. 5(F). By doingso, the large number of SRRs 16 are each covered entirely by silicondioxide films 24AP and 24BP. Then, in Step 112, the wafer P istransported to the coater/developer (not shown), and the firstphotoresist layer 22A (sacrifice layer) on the wafer P is dissolved andremoved. In order to remove the first photoresist layer 22A, it isallowable to perform the plasma ashing. With this, as shown in FIG.5(G), a large number of resonating elements 14, each of which isconstructed of the SRR 16 covered by the protective layer 18 which isformed of the silicon dioxide films 24AP and 24BP, are produced in astate that the resonating elements 14 are separated from the wafer P.The powder 12 shown in FIG. 1(A) is obtained by collecting the largenumber of resonating elements 14 produced on one lot of the wafers P.

Note that in a case of producing further a greater number of theresonating elements 14, it is possible to re-use the one lot of wafersused in the production steps as described above. Accordingly, the wafersare not burden on the production cost.

Afterwards, in a case of producing the liquid 30 (optical liquid) shownin FIG. 6(A), the powder composed of the large number of resonatingelements 14 is dissolved in a solvent 30 a such as water, etc. inside apredetermined container in Step 121, followed by being agitated with anagitating device (not shown), as necessary.

On the other hand, in a case of producing the optical element 32 asshown in FIG. 6(C), the powder composed of the large number ofresonating elements 14 is placed in a predetermined mould, followed bybeing sintered in Step 131. In this procedure, it is also allowable topreviously and uniformly mix the powder of the resonating elements 14and the medium 32 a in a powdery state (filling agent).

The effects, etc. of the embodiment are as follows.

(1) The powder 12 of the embodiment is an optical material which is usedas a component (a part or a portion) of a liquid or solid to which theillumination light is irradiated and includes a large number of theresonating elements 14; the resonating elements 14 are each formed bycovering the minute SRR (split-ring resonator) 16 made of the metal(conductor) having the width smaller than the wavelength of theillumination light with the protective layer 18 formed of silicondioxide, etc. (insulator).

According to the optical material of the embodiment, the SRR 16 isformed to have the size or dimension not more than about the wavelengthof the visible light, thereby making it possible that the SRR 16 has thereal part of the relative permeability different from 1 to a lighthaving a wavelength which is in the infrared region or smaller than theinfrared region. Further, since each of the SRRs 16 is covered by theprotective layer 18, the plurality of SRRs 16 do not contact with oneanother, and thus are structurally stable.

Note that it is allowable to use, as the material for the protectivelayer 18, a semi-conductor such as silicon nitride (Si₃N₄), etc., otherthan the insulator.

(2) Further, in the large number of resonating elements 14 constructingthe powder 12, the real part of the relative permeability (andconsequently permeability) of the SRR 16 with respect to theillumination light may be negative and the real part of the relativepermittivity (and consequently permittivity) of the protective layer 18which covers each of the SRRs 16 with respect to the illumination lightmay be negative. With this, the resonating elements 14 or the liquid orsolid containing the resonating elements 14 therein becomes an opticalmaterial having a negative refractive index to the illumination light.

(3) Further, the liquid 30 obtained by dissolving the powder 12 in thesolvent 30 a can be used as an optical liquid having, for example, arefractive index greater than 2 or having a negative refractive index.

(4) Furthermore, the optical element 32 formed by solidifying the powder12 can be used as the optical material having, for example, a refractiveindex greater than 2 or having a negative refractive index.

(5) Moreover, the method for producing the large number of resonatingelements 14 of the embodiment includes: Step 101 of forming the firstphotoresist layer 22A (sacrifice layer) on the wafer P; Step 102 offorming the first silicon dioxide layer 24A on the first photoresistlayer 22A; Step 103 of forming the metallic thin film 26 on the firstsilicon dioxide film 24A; Steps 104 to 107 of patterning the pluralityof SRRs 16 on the thin film 26; Steps 108 to 111 of forming the secondsilicon dioxide layer 24B so as to cover the plurality of SRRs 16; andStep 112 of removing the first photoresist layer 22A.

Accordingly, it is possible to mass-produce the powder 12 composed ofthe large number of resonating elements 14 of the embodiment with highprecision by using the photolithography step.

(6) Further, the step of forming the second silicon dioxide layer 24Bincludes Steps 109 to 111 of removing the silicon dioxide layers 24A,24B between the plurality of SRRs 16. Accordingly, by removing the firstphotoresist layer 22A next, the plurality of resonating elements 14 canbe separated easily from one another.

(7) Furthermore, the optical liquid 30 shown in FIG. 6(A) can beproduced by the step of mixing the powder 12 composed of the largenumber of resonating elements 14 in the solvent 30 a (liquid such aswater, etc.); and the step of agitating the solvent 30 a in which thepowder 12 is mixed. Accordingly, the liquid can be produced easily.

(8) Moreover, the optical element 32 shown in FIG. 6(C) can be producedby including the step of sintering the powder 12 composed of the largenumber of resonating elements 14. Accordingly, the optical element 32can be produced easily.

Note that the following modifications can be made for the embodimentdescribed above.

(1) It is allowable to use, instead of the resonating element 14 of theembodiment, a resonating element 14A (split-ring resonator provided witha protective film) having a construction in which a double split-ringresonator 17 is covered with the protective layer 18, as in a firstmodification shown in FIG. 7(A). As shown in FIG. 7(B), the split-ringresonator 17 is obtained by surrounding a first split-ring 17A having aradius of r and a width of w in the radial direction with a secondsplit-ring 17B having a width of w at a spacing distance or gap g.Further, the thickness of each of the split-rings 17A, 17B is T. Thisresonating element 14A can also be easily produced by a productionmethod similar to the production method of FIG. 3. Accordingly, theconstruction of the SRR (split-ring resonator) is arbitrary.

(2) Further, in a case that the image of the pattern of the firstreticle R1 shown in FIG. 4(B) is exposed in Step 105 of FIG. 3 by using,for example, a dry-type exposure apparatus of which resolution is lowerthan that of the liquid-immersion type exposure apparatus 50 of theabove-described embodiment, there is a fear that the resolution mightnot be sufficient. In such a case, it is allowable to divide the largenumber of first patterns 55 of the reticle R1 into two simpler-shapedpatterns and to perform double-exposure with these two divided patterns.By doing so, it is possible to produce the large number of resonatingelements 14 including the minute SRRs 16 highly precisely by using anexposure apparatus having a low resolution. As an example, the largenumber of first patterns 55 of the reticle R1 can be divided intocircular patterns (annular patterns) 551 (first portion) constructed ofa large number of light-shielding films formed on a reticle R1A of FIG.8(A); and a pattern (second portion) which is formed in alight-shielding film of a reticle R1B of FIG. 8(B) and which includes,as light-transmitting portions, a plurality of vertical line patterns553, a plurality of horizontal line patterns 554 and a large number ofsmall circular patterns 552 each arranged at the intersection of theline patterns 553 and 554. The patterns of the reticles R1A and R1B ofthe second modification are simpler than the pattern of the reticle 1and the pattern period is wide, which in turn makes it possible toexpose the patterns of the reticles R1A and R1B on the wafer with arequired resolution with an exposure apparatus having a lower resolutionthan that of the exposure apparatus 50.

Note that the large number of first pattern 55 of the reticle R1 may bedivided into two or more patterns having simpler shapes, and the two ormore simpler-shaped pattern may be subjected to the multiple-exposure.

(3) Further, in a case of producing the optical element 32 of FIG. 6(C),it is allowable to use, as the medium 32 a to be mixed with the largenumber of resonating elements 14, a solid obtained by solidifying aliquid in the sol state by the Sol-Gel process. The Sol-Gel process is achemical reaction in which the sol is turned into the gel state byheating, etc. and then ceramics, etc., is synthesized. In this casealso, in the step of mixing the large number of resonating elements 14(powder 12) and the medium 32 a, the medium 32 a is a liquid in the solstate, and thus the large number of resonating elements 14 and themedium 32 a can be mixed uniformly.

As the liquid in the sol state for the medium 32 a, it is possible touse, as an example, tetraethoxysilane (Si(OR₄). Here, —OR is ethoxygroup (—OC₂H₅), and —R is ethyl group (—C₂H₅). The reaction in this caseis, for example, as follows.

At first, when the powder 12 of the resonating elements 14 is mixed to apure water solution (Sol) of tetraethoxysilane and is then heated, theaqueous solution of tetraethoxysilane becomes colloid of triethoxysilanehydroxide and ethanol as follows, due to the hydrolysis. The heatingtemperature is, for example, 600 degrees Celsius to 1,100 degreesCelsius, and ethanol is evaporated and recovered.

Si(OR)₄+H₂O+Powder→Si(OR)₂(OH)+ROH+Powder  (11A)

When the hydrolysis is continued further, the triethoxysilane hydroxide,uniformly mixed with the powder (resonating elements 14) assumes astructure such as that of silicon dioxide, due to the followingpolymerization reaction.

2×Si(OR)₃(OH)+Powder→(OR)₃Si—O—Si(OR)₃+H₂O+Powder  (11B)

Accordingly, in the optical element 32 which is finally formed, theresonating elements 14 and the solvent 32 a are uniformly mixed and therefractive index of the medium 32 a is approximately same as therefractive index of the protective layer 18 (provided that theprotective layer 18 is formed of silicon dioxide) of the resonatingelements 14. Therefore, the reflection on the interface is lowered andthe transmittance with respect to the illumination light becomes high.

Note that in this reaction, when the amount of the pure water is toomuch and the concentration of the solid in the solvent 32 a is small,then the pure water may be evaporated.

(4) Further, in the resonating elements 14 of the embodiment describedabove, the real part of the permittivity is positive and the real partof the relative permittivity is also positive (for example, real numbergreater than 1). Therefore, even when a large number of the resonatingelements 14 are merely collected, the refractive index remains to bepositive.

In view of this, as a resonating element 14B of a third modificationshown in FIG. 9(A), it is allowable to form a pair of line patterns 81Xelongated in the y-direction and a pair of line patterns 81Y elongatedin the x-direction so as to sandwich (interpose) each of the SRRs(split-ring resonators) 16 therebetween in the x-direction and they-direction, respectively, inside the protective layer 18. The linepatterns 81X, 81Y are minute thin lines formed of a conductor (metal,etc.) which is same as that forming the SRR 16.

In this modification, it is assumed that the wavelength of a light(light beam) ILY is within a range in which the real part μRe of therelative permeability of FIG. 2 takes a negative value (for example, avalue slightly smaller than the wavelength λ3) provided that the lightILY is a light in which a vibration direction EVY of the electric fieldvector is parallel to the x-axis (linearly polarized in the x-direction)and the vibration direction of the magnetic field vector is parallel tothe z-axis and that the light ILY comes into the resonating element 14Bin the y-direction. In this case, the line width (cross-sectional area)and the length in the x-direction of the line pattern 81Y and thearrangement such as the x-direction and y-direction period, etc. of thelarge number of line patterns 81Y are set so that the real part of thepermittivity of the resonating elements 14B to the light ILY is negative(the real part of the relative permittivity is also negative).

As a result, the resonating element 14B (or a substance obtained bycollecting the resonating elements 14B) becomes a meta-material in whichthe refractive index to the light ILY takes a negative value.

Note that an example of construction of the plurality of thin metalliclines, in which the real part of the permittivity is negative withrespect to a microwave, is described in Literature by D. R. Smith et al.and entitled “Composite medium with simultaneously negative permeabilityand permittivity”, Phys. Rev. Lett. (the United States), 84, pp.4184-4187 (2000) (hereinafter referred to as “Reference Literature B”).The line patterns 81Y of the modification shown in FIG. 9(A) is formedto have the minute shape and arrangement so that the real part of thepermittivity to the visible light takes a negative value.

Further, it is presumed that the shape and arrangement of the largenumber of line patterns 81X elongated in the y-direction inside theresonating element 14B are same as the shape and arrangement of the linepatterns 81Y. In this case, when a light ILX (provided that the lightILX has a wavelength same as that of the light ILY), in which avibration direction EVX of the electric field vector is parallel to they-axis (linearly polarized in the y-direction) and the vibrationdirection of the magnetic field vector is parallel to the z-axis, comesinto the resonating element 14B in the x-direction, then the real partof the permittivity of the resonating element 14B to the light ILX alsobecomes negative, due to the line pattern 81X. Accordingly, therefractive index of the resonating element 14B to the light ILX alsotakes a negative value. Therefore, by mixing the large number ofresonating elements 14B in the liquid or by solidifying the large numberof resonating elements 14B to thereby form an optical element, it ispossible to produce an optical liquid or optical element having anegative refractive index to a light having a predetermined wavelength.

Next, in a case that the resonating element 14B of FIG. 9(A) isproduced, it is allowable to use, in Step 105 of FIG. 3, a reticle R3 inwhich line patterns 58X, 58Y formed of a light-shielding film andcorresponding to the line patterns 81X, 81Y are formed around each ofthe first patterns 55 as shown in FIG. 9(B), instead of using thereticle R1 of FIG. 4(B).

By doing so, the line patterns 81X, 81Y can be patterned together and atthe same time with the large number of SRRs 16 in the metallic thin film26 of the wafer P.

Second Embodiment

Next, a second embodiment will be explained with reference to FIGS. 10to 16. In the following description, components or parts which are shownin FIGS. 10(A) to 12(B) and FIGS. 14(A) to 16 and which correspond tothose shown in FIGS. 1(A) to 1(C) and FIGS. 4(B) to 13, are designatedby the same reference numerals, and any detailed explanation thereforwill be simplified or omitted.

FIG. 10(C) shows powder 12A of an optical material of the secondembodiment. The powder 12A is obtained by collecting a large number ofminute resonating elements 14C or 14D. FIG. 10(A) is an enlargedperspective view of one resonating element 14C constituting the powder12A, and FIG. 10(B) is a side view of the resonating element 14C shownin FIG. 10(A). In FIG. 10(A), there is assumed x-axis and y-axis in arectangular coordinate system in a plane, and z-axis is assumed as anaxis perpendicular to the plane. The resonating element 14C isconstructed by covering a plurality of minute split-ring resonators 16(or SRRs 16), which are arranged in the x-direction and the y-directionat a period (pitch) of “a” to be arranged in K rows×L columns, with arectangular plate-shaped protective layer 18A composed of an insulatorsuch as silicon dioxide (SiO₂), aluminum oxide (Al₂O₃), or the like.

“K” is an arbitrary integer not less than 1, and “L” is an arbitraryinteger not less than 2. Note that K and L may be same integers not lessthan 2. In the embodiment, as an example, K=L=10. In this case, 100pieces of the SRR 16 are arranged in 10 rows×10 columns in theresonating element 14C. Note that the protective layer 18A may be, forexample, formed such that four corner portions thereof are rounded. Eachof the SRRs 16 is made of a metal such as silver (Ag), gold (Au), copper(Cu) or aluminum (Al), etc., and has a shape obtained by dividing a ringaxisymmetric with respect to an axis parallel to the z-axis into fourportions (see FIG. 12(B)). As shown in FIG. 10(B), a thickness (width inthe z-direction) T of the SRR 16 is smaller than the pitch “a”, and athickness Tp of the protective layer 18A is about three times thethickness T.

Note that it is allowable to use a resonating element 14D as shown inFIG. 11(A) and having a plurality of layers each including a pluralityof the SRRs 16 as the optical material for the powder 12A as shown inFIG. 10(C), instead of using the resonating element 14C as shown in FIG.10(A) and having one layer of the plurality of SRRs 16 formed therein.In FIG. 11(A), the resonating element 14D is obtained by covering, withthe protective layer 18A, a plurality of SRRs 16 which are arranged atthe period (pitch) of “a” in K rows×L columns in the x-direction and they-direction and are arranged in M layers such as a first layer 15A, asecond layer 15B, a third layer 15C, etc., in the z-direction at aperiod (pitch) of “b”. In this case, K is an arbitrary integer not lessthan 1, L and M are each an arbitrary integer not less than 2. Note thatK and L may be same integers not less than 2, and that the resonatingelement 14C shown in FIG. 10(A) corresponds to the arrangement in whichM=1.

As shown in the side view of FIG. 10(B), the thickness Tp3 of theprotective layer 18A of the resonating element 14D is approximately (3×T+(M−1)b). Note that in FIG. 11(A), the resonating element 14D has athree-layered structure (L=3). Other than this, as an example, therelationship among K, L and M may be K=L=M=10. In such a case, 1000pieces of the SRRs 16 are arranged in 10 rows×10 columns×10 layers inthe resonating element 14D.

FIG. 12(A) is an enlarged view showing a portion of the resonatingelement 14D (note that the resonating element 14D has a two-layeredstructure). The resonating element 14D can be considered as a pluralityof the resonating elements 14C which are overlaid (stacked) in thez-direction. Note that although the large number of resonating elements14D in the powder 12A of FIG. 10(C) are arranged randomly, theresonating elements 14D approximately arranged as shown in FIG. 12(A)are included in the powder 12A at a certain ratio.

FIG. 12(B) shows one of the SRRs (split-ring resonators) 16 shown inFIG. 12(A). The shape and material of the SRR 16 is same as those of theSRR 16 shown in FIG. 1(B) of the first embodiment. Namely, in FIG.12(B), the SRR 16 is constructed of four fan-shaped members 16A, 16B,16C and 16D obtained by splitting or dividing a ring, which has an innerradius r, a width w in the radial direction and a thickness T, in thecircumference direction of the ring with a spacing distance g. Note thata split number N (N=2, 3, 4, 5, by which the SRR is split is arbitrary.

The arrangement of the plurality of SRRs 16, in the resonating element14D of FIG. 12(A), on the rectangular coordinate system (x, y, z) issame as the arrangement of the plurality of SRRs 16 in the resonatingelement 14 of FIG. 1(B) of the first embodiment. Accordingly, similarlyto the first embodiment, the effective relative permeability μeff of theplurality of SRR 16 arranged as shown in FIG. 12(A) with respect to anillumination light having a predetermined wavelength λ (provided thatthe angular frequency is ω) is represented by the formula (1).

According to the formula (1), the real part μRe of the effectiverelative permeability μeff becomes considerably greater than 1 in thepredetermined ranges in each of which the frequency f [THz] of theillumination light is smaller than the predetermined resonance frequency(f1, f2, f3, etc.) and takes a negative value in the predeterminedranges in each of which the frequency f is greater than thepredetermined resonance frequency, as shown in FIG. 2, depending on theshape and arrangement of the SRRs 16. Furthermore, as the resonancefrequency f becomes higher from f1 to f3, the absolute value of the realpart μRe becomes smaller. Note that the resonance frequency issubstantially defined by the parameters of the shape of SRR 16 (r, w, T,etc.), and the contribution by the arrangement periods a, b of the SRRs16 are considered as relatively small.

Similarly to the first embodiment, according to Reference Literature A,in a case that the radius r of the SRR 16 is same as the width w of theSRR 16, the period b is 350 nm, the spacing distance g is 33 nm, thethickness T is 2.5 times the penetration depth, and the relativepermittivity ∈r is 2.25, the resonance frequency f1 is 300 THz (thewavelength λ1 corresponding thereto is 1000 nm (1 μm)), the resonancefrequency f2 is 500 THz (the wavelength λ2 corresponding thereto is 600nm), and the resonance frequency f3 is 700 THz (the wavelength λ3corresponding thereto is 420 nm).

Further, the period a, the radius r and the outer diameter 4r in theformulae (1) to (5) when the resonance frequency f3 (the wavelength λ3:420 nm) can be obtained are 350 nm, 50 nm and 200 nm, respectively. Inthis case, since the thickness T of the SRR 16 is approximately same asor thinner than the radius r, the maximum width of the outer shape ofthe SRR 16 is 4r, and the size or dimension of the outer shape (themaximum width (4r)) of the SRR 16 is approximately ½ of the wavelengthsλ1 to λ3 corresponding thereto.

As described above, provided that the arrangement of the SRRs 16 in theresonating element 14D is 100 rows×100 columns×100 layers in a case thateach of the periods a and b are 350 nm, then the size of the resonatingelement 14D is approximately 35×35×35 μm³. Accordingly, the resonatingelement 14C, 14D has a size of μm-order, and thus the resonating element14C, 14D can be easily handled, thereby making it possible to suppress,for example, inadvertent aggregation of a plurality of the elements.

Further, in the embodiment, in a cases that the relative permittivity ofthe protective layer 18A is approximately 1 and that the resonatingelements 14C (or 14D) are used as a substance having the real part μReof the relative permeability which is considerably greater than 1 (forexample, greater than 2), the wavelength of the illumination light maybe set, for example, to λ1 b, λ2 b (frequencies f1 b, f2 b correspondingthereto are lower than the resonance frequencies f1, f2), etc. in arange slightly longer than λ1, λ2 (similarly regarding λ3 as well). Onthe other hand, in a case that the resonating elements 14C (or 14D) areused as a substance having the real part μRe of the relativepermeability that is negative, the wavelength of the illumination lightmay be set to λ1 a, λ2 a (frequencies f1 a, f2 a corresponding theretoare higher than the resonance frequencies f1, f2), etc. in a rangeslightly shorter than λ1, λ2. By doing so, the resonating element 14D(or 14C) can be used as a substance (meta-material) in which the realpart μRe of the relative permeability is considerably different from 1.

As an example shown in FIG. 6(A), a large number of the resonatingelements 14C (or 14D) may be mixed (or dissolved) in a predeterminedsolvent to thereby produce an optical liquid 30. The liquid 30 isobtained, for example, by mixing (dissolving) a large number of theresonating elements 14C (or 14D) in a solvent such as a pure water(purified water). Further, in a case that the solvent is water (relativepermittivity is positive), the resonating elements 14C are used, forexample, under a condition that the wavelength is set to be λ1 b or λ2b, etc. with which the real part μRe of the relative permeability isconsiderably greater than 1 as shown in FIG. 2. Under this condition,since the refractive index of the water 30 is greater than, for example,2, the liquid 30 can be used as a liquid having a high refractive index.Such a liquid having the high refractive index is usable, for example,as an immersion liquid for a liquid immersion type microscope, animmersion liquid for a liquid immersion type exposure apparatus (to bedescribed later on), etc. The orientations (directions) of therespective resonators mixed in the liquid are random, and thus theliquid can have an isotropic optical characteristic.

Further, in a case that the solvent is, for example, a liquid having anegative relative permittivity, the resonating elements 14C (or 14D) areused, for example, under a condition that the wavelength is set to be λ1a or λ2 a, etc. with which the real part μRe of the relativepermeability is negative as shown in FIG. 2. Under this condition, therefractive index of the liquid 30 takes a negative value. Such a liquidhaving the negative refractive index is, for example, filled in a celland thus becomes usable as a super lens such as an optical elementhaving a negative refractive index, as will be described later on.

Furthermore, as shown in FIG. 6(C) as another example, a plate-shapedoptical element 32 can be produced by solidifying the large number ofresonating elements 14C (or 14D). The optical element 32 is obtained,for example, by mixing a medium in a powdery form (filling agent) andthe powder of the resonating elements 14C, 14D uniformly and then bysolidifying the mixture by means of sintering, etc. Further, in a casethat the protective layer 18A of each of the resonating elements 14C,14D is formed of silicon dioxide (having positive relative permittivity)in a state that the medium is absent, then the resonating elements 14C,14D are used under a condition that the wavelength is set to be λ1 b orλ2 b, etc. with which the real part μRe of the relative permeability isconsiderably greater than 1 as shown in FIG. 2. Under this condition,since the refractive index of the optical element 32 takes, for example,a value greater than 2, it is possible to produce an optical lenshaving, for example, a refractive index greater than 2 by processing theoptical element 32 into a spherical or aspherical lens.

On the other hand, in a case that the medium is, for example, asubstance having a negative relative permittivity (for example, a largenumber of minute thin metallic lines, or a dielectric having a smallbandgap), the resonating elements 14C (or 14D) are used, for example,under a condition that the wavelength is set to be λ1 a or λ2 a, etc.with which the real part μRe of the relative permeability is negative asshown in FIG. 2. Under this condition, the refractive index of theoptical element 32 takes a negative value. When an illumination light ILcomes into such an optical element 32 having the negative refractiveindex from an external object point 34 as shown in FIG. 6(C), then theillumination light IL is imaged precisely to an external image point 36.Accordingly, the optical element 32 can be used as a so-called superlens.

Next, an example of a method for producing the powder 12A composed ofthe large number of single-layered resonating elements 14C as shown inFIG. 10(A) or the large number of multi-layered resonating elements 14Das shown in FIG. 11(A) will be explained with reference to a flow chartshown in FIG. 13 (FIGS. 13A, 13B). This producing method uses aphotolithography step, and the exposure apparatus 50 of theliquid-immersion type and shown in FIG. 4(A) is used in thephotolithography step. Since the exposure apparatus 50 is a liquidimmersion-type exposure apparatus as described above, the SRRs(split-ring resonators) 16 having the diameter r of about 50 nm in FIG.12(B) can be produced easily and highly precisely.

Further, FIG. 14(B) is an enlarged plane view showing a part or portionof a pattern formed in a pattern area in a first reticle R4 used in theexposure apparatus 50 shown in FIG. 4(A). In FIG. 14(B), first patterns56, each of which is formed of a light-shielding film and ismagnification of the SRRs 16 arranged for example in 10 rows×10 columnsin the resonating element 14C as shown in FIG. 10(A) by the reciprocalratio of the projection magnification β, are formed in the pattern areaof the reticle R4 while being arranged in mutually orthogonal twodirections at a predetermined spacing distance. Each of the firstpatterns 56 is formed by arranging a ring-shaped pattern 55, which isformed of a split-ring shaped, light-shielding film as shown in FIG.14(A) that is an enlarged view and corresponding to one piece of theSRRs 16, for examples in 10 rows×10 columns.

FIG. 14(C) is an enlarged plan view showing a part or portion of apattern formed in a second reticle R5 which is used in the exposureapparatus 50. In FIG. 14(C), second patterns 57A, each of which isformed of a light-shielding film and is magnification of the outer shapeof the protective layer 18A on the xy-plane of the resonating element14C, 14D by the reciprocal ratio of the projection magnification β, areformed in the pattern area of the reticle R5 while being in mutuallyorthogonal two directions at a predetermined period which is same as thearrangement period for the first patterns 56. During the exposure, eachof the second patterns 57A on the reticle R5 is positioned at a locationsame as a location 56A (including locations 55A at which a large numberof the ring-shaped patterns 55 are arranged respectively) at which oneof the first patterns 56 on the reticle R4 is arranged. Further, an areabetween the second patterns 57A on the reticle R5 corresponds to aseparation band for separating the plurality of resonating elements 14C,14D away from one another.

Further, in Step 141 of FIG. 13, one lot of wafers each of which is, forexample, a silicon wafer having a disc-shape and diameter of 300 mm isprepared. Although the following processes or steps are sequentiallyexecuted for processing the one lot of wafers, the processes will beexplained as follows regarding one piece of the wafers P. FIGS. 15(A) to15(G) and FIGS. 16(A) to 16(G) are each an enlarged cross-sectional viewshowing a part of the construction of a multi-layered thin film(plurality of layered thin films) formed on the wafer P. At first, in athin-film forming apparatus (not shown), a first photoresist layer 22Ais formed on an entire surface of the wafer P as shown in FIG. 15(A).The first photoresist layer 22A is used not as a photosensitive layerfor forming a resist pattern, but is used as a sacrifice layer forseparating the large number of resonating elements 14C, 14D away fromthe wafer P at the end of the processes.

Next, in Step 142, a first silicon dioxide (SiO₂) layer 24A is formed onthe first photoresist layer 22A on the wafer P. Then, in Step 143, afirst metallic thin film 26A formed of a metal (in this case, forexample, silver or aluminum, etc.) on the first silicon dioxide layer24A. Next, in Step 144, a second, positive-type photoresist layer 22B isformed on the metallic thin film 26. The second photoresist layer 22Band the first photoresist layer 22A are different types from each other,and the first photoresist layer 22A is not dissolved by a developingliquid and a dissolving liquid for the second photoresist layer 22B (anda photoresist layer 22C, etc. which will be described later on). Next,in Step 145, the wafer P is loaded on the exposure apparatus 50 shown inFIG. 4(A), and the second photoresist layer 22B in each of all the shotareas on the wafer P is exposed with images of a large number of thefirst patterns 56 (a large number of images 55P of the ring-shapedpatterns 55 for the SRRs 16) of the reticle R4, by the exposureapparatus 50. Note that in this example, areas between the large numberof images 55P are exposed by the illumination light in FIG. 15(A).

Next, in Step 146, the wafer P is transported to a coater/developer (notshown), and the second photoresist layer 22B on the wafer P isdeveloped. By doing so, a resist pattern 22BP corresponding to the SRRs16 (images 55P) is formed, as shown in FIG. 15(B). Next, in Step 147,the wafer P is transported to an etching device (not shown) and themetallic thin film 26A on the wafer P is etched with the resist pattern22BP serving as a mask, thereby forming a large number of minute SRRs 16of the first layer 15A as shown in FIG. 15(C). Then, the resist pattern22BP is removed.

Next, in Step 148, in the thin-film forming apparatus (not shown), asecond silicon dioxide layer 24B is formed so as to cover the largenumber of minute SRRs 16 on the wafer P, as shown in FIG. 15(D). Next,in Step 149, a surface of the silicon dioxide layer 24B is planarized(flattened) by the chemical-mechanical polishing (CMP), as shown in FIG.15(E). Next, in Step 150, confirmation is made whether or not a layer ofthe SRRs 16 (here, a second layer of SRRs 16) is to be formed on thefirst layer 15A. In a case that the second layer is not to be formed,namely in a case that a single-layered resonating element 14C of FIG.10(A) is to be produced, then the procedure proceeds to Step 151. Here,provided that the second layer is to be formed, the procedure returns toStep 143 and a metallic thin film 26B which is same as the metallic thinfilm 26A is formed on the silicon dioxide layer 24B and then a thirdphotoresist layer 22C is formed on the metallic thin film 26B (Step144), as shown in FIG. 15(F). Next, the photoresist layer 22C in each ofall the shot areas on the wafer P is exposed with the large number ofimages of the first patterns 56 (images 55P of the ring-shaped patterns55) of the reticle R4, by the exposure apparatus 50.

Next, the photoresist layer 22C on the wafer P is developed (Step 146),thereby forming a resist pattern 22CP corresponding to the SRRs 16(images 55P), as shown in FIG. 15(G). Next, the metallic thin film 26Bon the wafer P is etched with the resist pattern 22CP serving as a mask(Step 147), thereby forming a large number of minute SRRs 16 of thesecond layer 15B as shown in FIG. 16(A). Then, the resist pattern 22CPis removed.

Next, a third silicon dioxide layer 24C is formed so as to cover thelarge number of SRRs 16 of the second layer 15B, as shown in FIG. 16(B)(Step 148). Next, a surface of the silicon dioxide layer 24C isplanarized as shown in FIG. 16(C). Next, in Step 150, provided that athird layer is not to be formed on the second layer 15B in this case,and the procedure proceeds to Step 151 in which a fourth, positive-typephotoresist layer 22D is formed on the silicon dioxide layer 24C of thewafer P in the coater/developer (not shown), as shown in FIG. 16D. Next,in Step 152, the wafer P is loaded on the exposure apparatus 50 shown inFIG. 4(A), and the photoresist layer 22D on the wafer P is exposed withthe images 57P of the second patterns 57 of the reticle R5, by theexposure apparatus 50. By doing so, the area (separation band) betweenthe large number of resonating elements 14D (or 14C, same as thefollowing description) on the wafer P is exposed. After that, thephotoresist layer 22D on the wafer P is developed in thecoater/developer (not shown). With this, as shown in FIG. 16(E), aresist pattern 22DP is formed at an area, at which the protective layer18A as shown in FIG. 11(A) or FIG. 10(A) is to be formed, so as to coverthe large number of the SRRs 16 in each of the resonating elements 14Don the wafer P.

Next, in Step 153, the plurality of silicon dioxide layers 22A to 24Care etched at the etching device (not shown) with the resist pattern22DP on the wafer P serving as a mask, as shown in FIG. 16(F). By doingso, the large number of SRRs 16 in the resonating element 14D are eachcovered entirely by the silicon dioxide films 24AP, 24BP and 24CP. Then,in Step 154, the wafer P is transported to the coater/developer (notshown), and the first photoresist layer 22A (sacrifice layer) isdissolved and removed. In order to remove the first photoresist layer22A, it is allowable to perform the plasma ashing. With this, as shownin FIG. 16(G), a large number of resonating elements 14D, eachconstructed of the large number of SRRs 16 of the first and secondlayers 15A, 15B which are covered by the protective layers 18A formed ofthe silicon dioxide films 24AP, 24BP and 24CP, are produced in a statethat the resonating elements 14D are separated from the wafer P. Notethat in a case wherein the second layer 15B is not formed, a largenumber of the resonating elements 14C is produced. The powder 12A shownin FIG. 10(C) is obtained by collecting the large number of resonatingelements 14D (or 14C) produced on one lot of the wafers P.

Note that in a case of producing a resonating element 14D includingthree or more layers of the large number of SRRs 16, the operations inSteps 143 to 149 may be repeated as the number of the layers. Further,note that in a case of producing further a greater number of theresonating elements 14C, 14D, it is possible to re-use the one lot ofwafers used in the production steps as described above. Accordingly, thewafers are not burden on the cost.

Afterwards, in a case of producing the liquid 30 (optical liquid) shownin FIG. 6(A), the powder composed of the large number of resonatingelements 14C or 14D is dissolved in a solvent 30 a such as water, etc.inside a predetermined container in Step 161, followed by being agitatedwith an agitating device (not shown), as necessary.

On the other hand, in a case of producing the optical element 32 asshown in FIG. 6(C), the powder composed of the large number ofresonating elements 14C or 14D is placed in a predetermined mould,followed by being sintered. In this procedure, it is also allowable topreviously and uniformly mix the powder of the resonating elements 14C,14D and the medium 32 a (filling agent) in a powdery state. Note that inthe powder 12A, the liquid 30 and the optical element 32, it isallowable to use a large number of the single-layered resonatingelements 14C and the large number of the multiple-layered resonatingelements 14D in a mixed manner.

The effects, etc. of the embodiment are as follows.

(1) The powder 12A of the embodiment is an optical material which isused as a component (a part or a portion) of a liquid or solid to whichthe illumination light is irradiated and includes the plurality ofminute resonating elements 14C, 14D; the resonating elements 14C, 14Deach include the plurality of SRRs (split-ring resonator) 16 made of themetal (conductor) having the width that is approximately same as orsmaller than the wavelength of the illumination light and arranged apartfrom one another and the protective layer 18A which is formed of silicondioxide, etc. (insulator) and which covers the plurality of SRRs 16.

According to the optical material of the embodiment, the SRR 16 isformed to have the size or dimension not more than about the wavelengthof the visible light, thereby making it possible that the SRR 16 has thereal part of the relative permeability different from 1 to a lighthaving a wavelength which is in the infrared region or smaller than theinfrared region. Further, since each of the SRRs 16 is covered by theprotective layer 18, the plurality of SRRs 16 do not contact with oneanother, and thus are structurally stable. Furthermore, since therelative positions of the plurality of SRRs 16 are substantially fixed,the characteristics such as the resonating frequencies f1 to f3, etc.can be easily controlled by controlling the relative positions.

Note that it is allowable to use, as the material for the protectivelayer 18A, a semi-conductor such as silicon nitride (Si₃N₄), etc., otherthan the insulator.

(2) Further, the plurality of SRRs 16 in the resonating element 14C arearranged at the period “a” along the x- and y-axes perpendicular to eachother; and the plurality of SRRs 16 in the resonating element 14D arearranged at the period “a” along the x- and y-axes perpendicular to eachother and arranged at the period b along the z-axis. Thus, according tothe resonating elements 14C or 14D, since the two-dimensional orthree-dimensional arrangement of the SRRs 16 are fixed, it is possibleto control the characteristics such as the resonating frequency, etc.,further easily and precisely.

(3) Furthermore, in the large number of resonating elements 14C, 14Dconstructing the powder 12A, the real part of the relative permeability(and consequently permeability) of the SRRs 16 with respect to theillumination light may be negative and the real part of the relativepermittivity (and consequently permittivity) of the protective layer 18Awhich covers the SRRs 16 with respect to the illumination light may benegative. With this, the resonating elements 14C, 14D or the liquid orsolid containing the resonating elements 14C, 14D therein becomes anoptical material having a negative refractive index to the illuminationlight.

(4) Moreover, the liquid 30 obtained by dissolving the powder 12A in thesolvent can be used as an optical liquid having a refractive index forexample greater than 2 or having a negative refractive index.

(5) Further, the optical element 32 formed by solidifying the powder 12Acan be used as the optical material having a refractive index forexample greater than 2 or having a negative refractive index.

(6) Furthermore, the method for producing the large number of resonatingelements 14C of the embodiment includes: Step 141 of forming the firstphotoresist layer 22A (sacrifice layer) on the wafer P; Step 142 offorming the first silicon dioxide layer 24A on the first photoresistlayer 22A; Step 143 of forming the metallic thin film 26A on the firstsilicon dioxide layer 24A; Steps 144 to 147 of patterning the pluralityof SRRs 16 on the thin film 26A; Steps 148 and 149 of forming the secondsilicon dioxide layer 24B so as to cover the plurality of SRRs 16; Steps151 to 153 of removing a portion or part of the silicon dioxide layer24A and a portion or part of the silicon dioxide layer 24B in accordancewith the arrangement of the SRRs 16; and Step 154 of removing the firstphotoresist layer 22A.

According to this producing method, it is possible to highly preciselymass-produce the powder 12A composed of the large number of resonatingelements 14C of the embodiment by using the lithography step.

(7) Further, between the operation of Step 148 performed for the firsttime and the operations of Steps 151 to 153, this producing method iscapable of performing Step 149 of planarizing (flattening) the surfaceof the silicon dioxide layer 24B, Step 143 of forming the secondmetallic thin film 26B on the silicon dioxide layer 24B which has beenplanarized, Steps 144 to 147 of patterning the plurality of SRRs 16 inthe second metallic thin film 26B, and Step 148 of forming the silicondioxide layer 24C so as to cover the plurality of SRRs 16 which havebeen patterned.

By repeating the operations of Steps 143 to 148 as described above, itis possible to produce the resonating elements 14D including a largenumber of the SRRs 16 arranged in multiple layers.

Note that following modifications can be made to the respectiveembodiments described above.

(1) First, it is allowable to apply (coat) a surfactant to surfaces ofthe protective layers 18, 18A of the respective resonating elements 14,14A to 14D of the respective embodiments. By doing so, it is possible toprevent the plurality of resonating elements 14, 14A to 14D from fixingto one another when the resonating elements 14, 14A to 14D are in thepowdery state.

(2) Next, instead of the first photoresist layer 22A on the wafer P inFIG. 5(A) of the first embodiment or the first photoresist layer 22A onthe wafer P in FIG. 15(A) of the second embodiment, it is allowable toform, for example, a layer of silicon dioxide as the sacrifice layer. Insuch a case, it is possible to use, for example, fluorinated acid as adissolving liquid for dissolving the sacrifice layer in Step 112 or Step154. Namely, the wafer P may be immersed in the fluorinated acid. As thematerial for forming the protective layer 18, 18A in this case (materialused instead of the material forming the silicon dioxide layers 24A to24C), it is allowable to use a material which is not dissolved by thefluorinated acid, such as silicon nitride, aluminum oxide or aluminumnitride (AlN), etc.

(3) Further, instead of using the SRRs 16 inside the resonating elements14C, 14D of the second embodiment, it is allowable to use the doublesplit-ring resonator 17 shown in FIG. 7(B), in a similar manner as inthe first embodiment. A resonating element in which a plurality ofdouble split-ring resonators 17 are covered by the protective film 18A,etc., can also be easily produced by a producing method similar to theproducing method of FIG. 13. Accordingly, the construction of thesplit-ring resonator is arbitrary.

(4) Furthermore, in the second embodiment, in a case that the exposureis performed with the image of the pattern of the first reticle R4 shownin FIG. 14(B) in Step 145 of FIG. 13 by using, for example, a dry-typeexposure apparatus of which resolution is lower than that of theliquid-immersion type exposure apparatus 50, there is a fear that theresolution might not be sufficient. In such a case, it is allowable todivide the large number of ring-shaped patterns 55 of the reticle R4into two simpler-shaped patterns and to perform double-exposure withthese two divided patterns, in a similar manner to the first embodiment.By doing so, it is possible to produce the large number of resonatingelements 14C, 14D including the minute SRRs 16 highly precisely by usingan exposure apparatus having a low resolution.

Note that it is allowable to divide the large number of ring-shapedpatterns 55 of the reticle R4 into two or more pieces of simpler-shapedpatterns and to perform multiple-exposure with these two or more dividedpatterns.

(5) Moreover, in the first embodiment, in a case that a large number ofthe resonating elements 14, 14A, 14B are mixed in the solvent 30 a tothereby produce the liquid 30 as shown in FIG. 6(B) or in the secondembodiment, in a case that a large number of the resonating elements14C, 14D, etc. are mixed in the solvent 30 a to thereby produce theliquid 30, it is allowable to use, as the solvent 30 a, for example asolvent obtained by mixing a coloring matter which absorbs theillumination light in pure water (purified water) so that the real partof the permittivity of the solvent 30 a to the illumination light ismade to be negative. Since the coloring matter functions as a substancehaving a negative permittivity, the refractive index of the liquid 30 tothe illumination light is negative when the real part of the relativepermeability of the resonating elements 14, 14A to 14D, etc. to theillumination light is negative.

(6) Further, in a case that the liquid 30 is produced by mixing thelarge number of resonating elements 14, 14A to 14D, etc. in the solvent30 a, the refractive index of the solvent 30 a may be made to be similarto the refractive index of the protective layers 18, 18A of theresonating elements 14, 14A to 14D. In a case that the protective layers18, 18A is formed of silicon dioxide, it is allowable to use, forexample, a hydrocarbon-based liquid (high-refractive index liquid) suchas decalin or dicyclohexyl, etc. as a solvent having the refractiveindex similar to that of silicon dioxide. By doing so, the differencebetween the refractive index of the solvent 30 a and the refractiveindex of the protective layers 18, 18A is made to be small, which inturn reduces the light loss (optical loss) due to the reflection of theillumination light at the interface between the solvent 30 a and theprotective layers 18, 18A.

(7) Furthermore, in a case that the optical element 32 is produced bymixing the large number of resonating elements 14, 14A and 14B with themedium 32 a (filling agent) of FIG. 6(D) and by solidifying the mixtureof the large number of resonating elements 14, 14A, 14B and the medium32 a in the first embodiment, or in a case that the optical element 32is produced by mixing the large number of resonating elements 14C, 14Dwith the medium 32 a (filling agent) and by solidifying the mixture ofthe large number of resonating elements 14C, 14D and the medium 32 a inthe second embodiment, it is allowable to use, as the medium 32 a, athermo-curable resin such as silicon resin. In this case, by performinga step of mixing the thermo-curable resin in liquid form and a largenumber of the resonating elements 14, 14A to 14D followed by beinguniformly agitated and a step of heating the mixture to solidify thethermo-curable resin, it is possible to easily produce an opticalelement 32 in which the large number of resonating elements 14, 14A to14D and the solid medium 32 a are uniformly mixed.

(8) Moreover, in the second embodiment, it is allowable to use, as themedium 32 a which is to be mixed with a large number of the resonatingelements 14C (or 14D), a solid obtained by solidifying a liquid in thesol state by the Sol-Gel process, similarly in the first embodiment.

(9) Further, in the resonating elements 14C, 14D of the secondembodiment, the real part of the permittivity is positive and the realpart of the relative permittivity is also positive (for example, realnumber greater than 1). Therefore, even when a large number of theresonating elements 14C, 14D are merely collected, the refractive indexremains to be positive.

In view of this, similarly as in the first embodiment, as a resonatingelement 14E of a modification shown in FIG. 17(A), it is allowable toform line patterns 81X elongated in the y-direction and line patterns81Y elongated in the x direction so as to sandwich (interpose), in they-direction and the x-direction, each of a large number of SRRs(split-ring resonators) 16, which are arranged inside the protectivelayer 18A along the x-axis and y-axis at the period “a”, therebetween.The line patterns 81X, 81Y are minute thin lines formed of a conductor(metal, etc.) which is same as that forming the SRR 16.

In this modification, it is assumed that the wavelength of the light ILYis within a range in which the real part μRe of the relativepermeability of the light ILY of FIG. 2 takes a negative value (forexample, a value slightly smaller than the wavelength λ3) provided thatthe light ILY is a light in which the vibration direction EVY of theelectric field vector is parallel to the x-axis (linearly polarized inthe x-direction) and the vibration direction of the magnetic fieldvector is parallel to the z-axis and that the light ILY comes into theresonating element 14E in the y-direction. In this case, the line width(cross-sectional area) and the length in the x-direction of the linepattern 81Y and the arrangement such as the x-direction and y-directionperiod, etc. of the large number of line patterns 81Y are set so thatthe real part of the permittivity of the resonating elements 14E to thelight ILY is negative (the real part of the relative permittivity isalso negative).

As a result, the resonating element 14E (or a substance obtained bystacking the resonating elements 14E in the z-direction) becomes ameta-material in which the refractive index to the light ILY takes anegative value. Note that the example of construction of the pluralityof thin metallic lines having a negative real part of the permittivitywith respect to the microwave is disclosed in Reference Literature B asdescribed above. The line patterns 81Y of the modification shown in FIG.17(A) is formed to have the minute shape and arrangement so that thereal part of the permittivity to the visible light takes a negativevalue.

Further, it is presumed that the shape and arrangement of the largenumber of line patterns 81X elongated in the y-direction inside theresonating element 14E are same as the shape and arrangement of the linepatterns 81Y. In this case, when a light ILX (presumed as having a samewavelength as that of the light ILY) in which the vibration directionEVX of the electric field vector is parallel to the y-axis (linearlypolarized in the y-direction) and the vibration direction of themagnetic field vector is parallel to the z-axis comes into theresonating element 14E in the x-direction, the real part of thepermittivity of the resonating element 14E to the light ILX also becomesnegative, due to the line pattern 81X. Accordingly, the refractive indexof the resonating element 14E to the light ILX also takes a negativevalue. Therefore, by mixing the large number of resonating elements 14Ein the liquid or by solidifying the large number of resonating elements14E to thereby form an optical element, it is possible to produce anoptical liquid or optical element having a negative refractive index toa light having a predetermined wavelength.

Also in the resonating element 14D of FIG. 11(A), it is possible to makethe real part of the permittivity of the resonating element 14D to thelight having the predetermined wavelength take a negative value byarranging a plurality of the line patterns formed of conductor in thevicinity of the respective SRRs 16. As a result, the refractive index ofthe resonating element 14D to the light having the predeterminedwavelength becomes negative.

Next, in a case that the resonating element 14E of FIG. 17(A) isproduced, it is allowable to use, in Step 145 of FIG. 13, a reticle R3in which line patterns 58X, 58Y formed of a light-shielding film andcorresponding to the line patterns 81X, 81Y are formed around each ofthe ring-shaped patterns 55 as shown in FIG. 17(B), instead of using thereticle R4 of FIG. 14(B).

By doing so, the line patterns 81X, 81Y can be patterned together withthe large number of SRRs 16 in the metallic thin film 26A, 26B, etc.

Note that the present teaching is not limited to the above-describedembodiments, and may take a various kinds of construction orconfiguration within a scope without deviating from the gist oressential characteristics of the present teaching. Further, the contentsincluding the specification, the claims, the drawings and the abstractof each of U.S. Provisional Application Ser. No. 61/202,845 filed onApr. 10, 2009, Japanese Patent Application No. 2009-243438 filed on Oct.22, 2009 and Japanese Patent Application No. 2009-243439 filed on Oct.22, 2009 are incorporated herein by reference in their entireties.

It is theoretically possible to realize a substance having the relativepermeability greatly different from 1 to the lights in the infrared tovisible regions and further to realize a substance having the relativepermeability with a negative value to the lights in the infrared tovisible regions by using the conventional minute split-ring resonators.However, in order to apply the substance, for example, to a visiblelight, the split-ring resonators are formed to have a radius of aboutnot more than 100 nm, and there arises a problem of how to produce therespective split-ring resonators highly precisely and in a largequantity. Further, when simply producing a large number of split-ringresonators, there is a fear that these split-ring resonators might bebrought into contact with one another, and further that the structure ofthe split-ring resonators might be destroyed or damaged, thereby makingit impossible to exhibit a desired relative permeability characteristicwith respect to a light as the application objective of the split-ringresonators.

Further, when merely producing the minute split-ring resonators by usingthe lithography technique, the respective resonators are formed whilebeing aligned or arranged in a two-dimensional plane, which in turncauses a problem such that the obtained resonators as they are cannot beused as an optical material having a three-dimensional volume.Furthermore, even if two-dimensional planes, in each of which a largenumber of split-ring resonators are arranged, are stacked so that thestacked two-dimensional planes have a three-dimensional volume, therespective resonators are aligned in one and same direction(orientation), which in turn causes a problem such that the obtainedmaterial is anisotropic as an optical material and thus is not aisotropic optical material.

The present invention has been made in view of the above-describedsituation, and has an object to provide an optical material (a kind ofmeta-material) which is for example capable of having a relativepermeability different from 1 to a light having a wavelength in theinfrared region or shorter than the infrared region and which has astable structure, and to provide a liquid and solid (optical element)using the optical material.

Another object of the present invention is to provide a method capableof mass-producing such an optical material with high precision, and amethod for producing the liquid and solid using the optical material.

According to the optical material of the present invention, the minuteresonators are formed to have a size or dimension which is, for example,about not more than the wavelength of visible light, thereby making itpossible to realize the relative permeability which is different from 1to a light in the infrared region or a light having a wavelength shorterthan the infrared region. Further, since each of the minute resonatorsis covered by the protective film, the plurality of minute resonators donot make contact with each other, thereby realizing the stablestructure.

According to the method for producing the optical material of the fifthor sixth aspect of the present invention, it is possible to mass-producethe optical material of the first or second aspect of the presentinvention with high precision, by using, for example, thephotolithography process.

1. A method for producing an optical material composed of a plurality ofminute resonators each of which is formed of a conductor, and is coveredby a protective film formed of an insulator or a semi-conductor, themethod comprising: forming a sacrifice layer on a substrate; forming afirst protective layer formed of the insulator or the semi-conductor onthe sacrifice layer; forming a conductive layer formed of the conductoron the first protective layer; patterning the minute resonators in theconductive layer; forming a second protective layer formed of theinsulator or the semi-conductor so as to cover the patterned minuteresonators; and removing the sacrifice layer.
 2. The method forproducing the optical material according to claim 1, wherein the formingof the second protective layer includes a step of removing a portion ofthe second protective layer disposed between the minute resonators. 3.The method for producing the optical material according to claim 1,wherein the patterning of the minute resonators includes: forming aresist layer on the conductive layer; exposing the resist layer with animage of the minute resonators; developing the resist layer; and etchingthe conductive layer.
 4. The method for producing the optical materialaccording to claim 1, wherein the sacrifice layer is dissolved byfluorinated acid, and the first and second protective layers are layerswhich are not dissolved by the fluorinated acid; and the removing of thesacrifice layer includes immersing the substrate in a solution of thefluorinated acid.
 5. The method for producing the optical materialaccording to claim 3, wherein the exposing of the resist layer with theimage of the minute resonators includes double-exposing the resist layerwith an image of a first portion of the minute resonators and an imageof a second portion of the minute resonators.
 6. A method for producingan optical material having a plurality of optical elements each of whichis composed of a plurality of minute resonators formed of a conductorand is arranged apart from each other, and which are covered by aprotective film formed of an insulator or a semi-conductor, the methodcomprising: forming a sacrifice layer on a substrate; forming a firstprotective layer formed of the insulator or the semi-conductor on thesacrifice layer; forming a first conductive layer formed of theconductor on the first protective layer; patterning the minuteresonators in the first conductive layer; forming a second protectivelayer formed of the insulator or the semi-conductor so as to cover thepatterned minute resonators; removing a part of the first protectivelayer and a part of the second protective layer based on an arrangementof the minute resonators in each of the optical elements; and removingthe sacrifice layer.
 7. The method for producing the optical materialaccording to claim 6, comprising, between the forming of the secondprotective layer and the removing of the part of the first protectivelayer and the part of the second protective layer: planarizing a surfaceof the second protective layer; forming a second conductive layer, whichis formed of the conductor, on the second protective layer; patterningthe plurality of minute resonators in the second conductive layer; andforming a third protective layer formed of the insulator or thesemi-conductor so as to cover the plurality of minute resonators whichhave been patterned.
 8. The method for producing the optical materialaccording to claim 6, wherein the patterning of the minute resonators inthe first conductive layer includes patterning a plurality of linearpatterns, together with the minute resonators, in the first conductivelayer.
 9. The method for producing the optical material according toclaim 6, wherein the sacrifice layer is dissolved by fluorinated acid,and the first and second protective layers are layers which are notdissolved by the fluorinated acid; and the removing of the sacrificelayer includes immersing the substrate in a solution of the fluorinatedacid.
 10. A method for producing an optical liquid in which the opticalmaterial made by the method of claim 1 is mixed, the method comprising:mixing the optical material in a liquid; and agitating the liquid inwhich the optical material is mixed.
 11. A method for producing anoptical element including the optical material made by the method ofclaim 1, the method comprising sintering the optical material.
 12. Themethod for producing the optical element according to claim 11,comprising, before the sintering of the optical material, mixing theoptical material and a filling agent.
 13. A method for producing anoptical element containing the optical material made by the method ofclaim 1, the method comprising: mixing the optical material and athermo-curable resin; and heating and solidifying a mixture of theoptical material and the thermo-curable resin.
 14. A method forproducing an optical liquid in which the optical material made by themethod of claim 6 is mixed, the method comprising: mixing the opticalmaterial in a liquid; and agitating the liquid in which the opticalmaterial is mixed.
 15. A method for producing an optical elementincluding the optical material made by the method of claim 6, the methodcomprising sintering the optical material.
 16. The method for producingthe optical element according to claim 15, the method comprising, beforethe sintering of the optical material, mixing the optical material and afilling agent.
 17. A method for producing an optical element containingthe optical material made by the method of claim 6, the methodcomprising: mixing the optical material and a thermo-curable resin; andheating and solidifying a mixture of the optical material and thethermo-curable resin.